Question

I need help :(( please please easetriangle area ?​

Answer 1

Answer:

$\frac{25\sqrt{3}}{2}$

Step-by-step explanation:

The area of a triangle is given by $A=\frac{1}{2}bh$ where $b$ is the base of the triangle and $h$ is the height of the triangle. In a right triangle, the two legs will represent the base and height, both interchangeable.

In a 30-60-90 triangle, the sides are in the proportion $x:x\sqrt{3}:2x$, where $2x$ is the hypotenuse of the triangle and $x$ is the side opposite to the 30 degree angle. Since the hypotenuse of this triangle is given as 10, the leg opposite to the 30 degree angle is equal to $10\div 2=5$ and the leg adjacent to the 30 degree angle is equal to $5\sqrt{3}$.

Thus, the area of this triangle is equal to:

$A=\frac{1}{2}\cdot 5\cdot 5\sqrt{3}=\boxed{\frac{25\sqrt{3}}{2}}$